Solve x-2y+mx+9=0

$$x - 2 y + m x + 9 = 0$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=-\frac{x-2y+9}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }y=\frac{9}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-2y+mx+9=-x$$

Add 2y to both sides.

$$mx+9=-x+2y$$

Subtract 9 from both sides.

$$mx=-x+2y-9$$

The equation is in standard form.

$$xm=-x+2y-9$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-x+2y-9}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-x+2y-9}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{9-2y}{m+1}\text{, }&m\neq -1\\x\in \mathrm{C}\text{, }&y=\frac{9}{2}\text{ and }m=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2y to both sides. Anything plus zero gives itself.

$$x+mx+9=2y$$

Subtract 9 from both sides.

$$x+mx=2y-9$$

Combine all terms containing x.

$$\left(1+m\right)x=2y-9$$

The equation is in standard form.

$$\left(m+1\right)x=2y-9$$

Divide both sides by 1+m.

$$\frac{\left(m+1\right)x}{m+1}=\frac{2y-9}{m+1}$$

Dividing by 1+m undoes the multiplication by 1+m.

$$x=\frac{2y-9}{m+1}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{x-2y+9}{x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&x=0\text{ and }y=\frac{9}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-2y+mx+9=-x$$

Add 2y to both sides.

$$mx+9=-x+2y$$

Subtract 9 from both sides.

$$mx=-x+2y-9$$

The equation is in standard form.

$$xm=-x+2y-9$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{-x+2y-9}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{-x+2y-9}{x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{9-2y}{m+1}\text{, }&m\neq -1\\x\in \mathrm{R}\text{, }&y=\frac{9}{2}\text{ and }m=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 2y to both sides. Anything plus zero gives itself.

$$x+mx+9=2y$$

Subtract 9 from both sides.

$$x+mx=2y-9$$

Combine all terms containing x.

$$\left(1+m\right)x=2y-9$$

The equation is in standard form.

$$\left(m+1\right)x=2y-9$$

Divide both sides by 1+m.

$$\frac{\left(m+1\right)x}{m+1}=\frac{2y-9}{m+1}$$

Dividing by 1+m undoes the multiplication by 1+m.

$$x=\frac{2y-9}{m+1}$$